Comptes Rendus
no. 4
Number Theory
On Euler products and multi-variate Gaussians
[Sur les produits eulériens et les gaussiennes multidimensionnelles]

Présenté par : Alain Connes

Dennis A. Hejhal1, 2
1 Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden
2 School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
Comptes Rendus. Mathématique, Volume 337 (2003) no. 4, pp. 223-226.

Nous généralisons à plusieurs variables un résultat récent de A. Selberg concernant la distribution asymptotique de valeurs des produits Eulériens. Sous certaines hypothèses un développement asymptotique de type Edgeworth est établi.

In this Note, we extend a recent result of A. Selberg concerning the asymptotic value distribution of Euler products to a multi-dimensional setting. Under certain conditions, an asymptotic development of Edgeworth type is found.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00344-3
Dennis A. Hejhal 1, 2

1 Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden
2 School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA 
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Dennis A. Hejhal. On Euler products and multi-variate Gaussians. Comptes Rendus. Mathématique, Volume 337 (2003) no. 4, pp. 223-226. doi : 10.1016/S1631-073X(03)00344-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00344-3/

[1] A. Beurling On functions with a spectral gap, The Collected Works of Arne Beurling, 2, Birkhäuser, 1989, pp. 370-372

[2] P. Billingsley Probability and Measure, Wiley, 1986

[3] E. Bombieri; D. Hejhal On the distribution of zeros of linear combinations of Euler products, Duke Math. J., Volume 80 (1995), pp. 821-862

[4] H. Cramér Random Variables and Probability Distributions, Cambridge University Press, 1962

[5] A. Fujii On the zeros of Dirichlet L-functions I, Trans. Amer. Math. Soc., Volume 196 (1974), pp. 225-235

[6] A. Ghosh On Riemann's zeta function – sign changes of S(T) (H. Halberstam, ed.), Recent Progress in Analytic Number Theory, 1, Academic Press, 1981, pp. 25-46

[7] D. Hejhal On a result of Selberg concerning zeros of linear combinations of L-functions, Intern. Math. Res. Notices (2000), pp. 551-577

[8] W. Luo Zeros of Hecke L-functions associated with cusp forms, Acta Arith., Volume 71 (1995), pp. 139-158

[9] H. Montgomery; R. Vaughan Hilbert's inequality, J. London Math. Soc., Volume 8 (1974) no. 2, pp. 73-82 (especially p. 75)

[10] A. Selberg Old and new conjectures and results about a class of Dirichlet series, Collected Papers, 2, Springer-Verlag, 1991, pp. 47-63

[11] A. Selberg Contributions to the theory of the Riemann zeta function, Archiv for Math. og Naturv. B, Volume 48 (1946), pp. 89-155 (especially §§ 2, 3)

[12] A. Selberg Lectures on sieves, Collected Papers, 2, Springer-Verlag, 1991, pp. 65-247 (especially §§20, 21)

[13] K.-M. Tsang, The distribution of the values of the Riemann zeta function, Ph.D. dissertation, Princeton University, 1984

[14] J. Vaaler Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. (N.S.), Volume 12 (1985), pp. 183-216

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